For tissue products such as facial and bath tissue and paper towels, strength and softness are important properties to many consumers. The strength properties of a product can be expressed in terms of wet strength and dry strength. The dry strength is important from the standpoint of manufacturing, since the product must have sufficient strength to pass through various stages in the manufacturing process where the sheet is unsupported and under tension. In the case of paper towels, for example, the dry strength must also be sufficient to enable a towel sheet to be detached from a roll of perforated sheets without tearing and to perform tasks in the dry state without shredding. The wet strength is particularly important because towels are routinely used to wipe up spills. As such, it is necessary that the towel hold up in use after it has been wetted. The amount of wet tensile strength developed using conventional alkaline curing wet strength resins, such as polyamide-epichlorohydrin (PAE) resins (i.e. Kymene® resins from Ashland Inc., Covington, Ky.) has been found in practice to be a function of the dry tensile strength of the sheet. Depending upon the furnish, the resin addition level and the water chemistry conditions, the wet tensile strength is generally limited to about 30-40 percent of the dry tensile strength of the sheet. Thus, in order to make tissue or paper products with a high level of wet tensile strength, one has to also develop a high level of dry tensile strength. Unfortunately, tissues and towels with high dry tensile strengths also exhibit high stiffness and therefore poor hand feel properties since the properties of softness (as characterized by low stiffness) and strength are inversely related. As strength is increased (both wet and dry strength), softness is decreased. Conversely, as softness is increased, the strength is decreased. A high wet/dry strength ratio is desired to provide superior durability when wet, while at the same time exhibiting low stiffness and desirable handfeel properties when dry. Hence there is a need for a means to increase the wet strength/dry strength ratio while maintaining or decreasing the stiffness of the sheet.